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1d
comment cohomology of a variation of wreath product
Consider the maps $(z_1,\ldots,z_n,z_{\sigma(1)}, \ldots,z_{\sigma(n)}) \mapsto (tz_1,\ldots,tz_n,tz_{\sigma(1)}, \ldots,tz_{\sigma(n)})$ for $t \in [0,1]$: this is a homotopy between the identity map and the constant map $(0,0,\ldots,0)$.
2d
comment cohomology of a variation of wreath product
Are you sure you're asking the question you intended to ask? The space you wrote down is obviously contractible. You could insist that all $z_i$ are distinct but in this case you would obtain $n!$ copies of the usual configuration space of $n$ ordered points in $\mathbf C$.
2d
reviewed Close Diffusion Equation
2d
reviewed Close How to calculate a sequence in Maple
Nov
18
awarded  Nice Answer
Nov
16
awarded  Good Answer
Nov
13
awarded  Enlightened
Nov
13
awarded  Nice Answer
Nov
12
comment Framed version of braided monoidal category
You're right, they form a nonsymmetric operad. By the way, I think there are some things you might find useful in Nathalie Wahl's Ph.D. thesis.
Nov
12
comment Gerbes and Stacks
I don't really understand you so at least one of us is confused. The fiber over a point of $U_i$ is a groupoid with one object and morphism set $BGL(1)$.
Nov
12
answered Framed version of braided monoidal category
Nov
12
answered Gerbes and Stacks
Nov
11
comment List of Classifying Spaces and Covers
...and even if you find the previous example too silly, allowing yourself to work with stacks does give you several natural examples, like $\mathrm{SL}(2,\mathbf Z)$ acting on the upper half plane.
Nov
11
comment List of Classifying Spaces and Covers
Here's a really dumb non-answer (dumb enough that I only make it a comment), but sometimes I find it useful to think along these lines. Namely, if you permit yourself to think about topological stacks instead of topological spaces, you can take $EG = \ast$ (a single point) and $BG = [\ast/G]$ ($G$ any group). This is the universal and minimal choice of classifying space.
Nov
11
comment Synthetic vs. classical differential geometry
There's an interesting recent book by Paugam that you might like (although I've only looked briefly at a few chapters), "Towards the Mathematics of Quantum Field Theory". The goal of his book is to formulate QFT mathematically in the most "correct" way possible, which for him means in terms of SDG, diffeological spaces, and homotopical algebra.
Nov
10
comment The properness of a submersion
I don't think this completely answers the question. Consider e.g. $\mathbf R\setminus \{0\} \sqcup \{0\}$ with its natural map to $\mathbf R$, which is a nonproper map with compact connected fibers. To rule out a silly counterexample like this it seems one should use the submersion hypothesis (which your argument doesn't).
Nov
8
awarded  Nice Question
Nov
8
asked What's the dimension of the space of CM cusp forms?
Nov
6
answered why are motives more serious than “naive” motives?
Nov
4
accepted Which mapping class group representations come from algebraic geometry?